"TouchID requires your Password after 48 hours"
Update July 2016
Since posting this question, the message has changed to
Your passcode is required to enable Touch ID
& now has a documented answer at https://apple.stackexchange.com/a/245796/85275
I just spotted the above message for the first time today. I've had the phone 3 weeks [new 6s] & never spotted it before.
It's not something I need to 'fix' but I wonder if anyone knows what may trigger it; & why it took 3 weeks to ask me for the first time.
.. or, incidentally & totally opinion-based - why it thinks a 6-digit code is more secure than my fingerprint.
Does it do it 2 days after a reboot or OS update?
It's done it just one more time, which was perhaps 48h+ after the 9.1 update.
Current guess is it's "new to iOS 9" which is why people have been seeing it on older devices too.
I'm still convinced I get it once after every update - but it's something I just dismiss without thinking until later, when I've lost the train of thought that would allow me to 'accurately guesstimate' when it was last rebooted.